Question
Asked Feb 10, 2020
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A group of students are using resonance to determine the temperature of the air in their laboratory. They use a tunning fork producing a 256 Hz tone. The fork is placed near the opening of a tube filled with water. The water is slowly let out until a resonant mode is heard. (a) Calculate the air temperature if the height of the water level is 33.6 cm at first resonance. (b) Find the height of the water level when the first overtone is heard.

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Expert Answer

Step 1

(a) For resonance condition, the height of the water column is

Physics homework question answer, step 1, image 1

The velocity of the sound heard is

Physics homework question answer, step 1, image 2

Step 2

The speed at which sound travels is also dependent upon the temperature of the gas. For air it is approximately

Physics homework question answer, step 2, image 1

Compare equation (2) and (3) to solve for the air temperature.

Physics homework question answer, step 2, image 2

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